Let's analyze the sales patterns for both styles of headbands to determine the correct system of equations.
For style A:
- Sharon sold 40 headbands in the first month.
- The sales increase by 10% each month.
To model this mathematically:
- The initial sales are 40.
- With a 10% increase each subsequent month, the sales function can be written as
[tex]\[
s = 40 \times (1 + 0.10)^m = 40 \times (1.1)^m
\][/tex]
For style B:
- Sharon sold 20 headbands in the first month.
- The sales increase by 15% each month.
To model this mathematically:
- The initial sales are 20.
- With a 15% increase each subsequent month, the sales function can be written as
[tex]\[
s = 20 \times (1 + 0.15)^m = 20 \times (1.15)^m
\][/tex]
Therefore, the system of equations she can use to determine the number of months, [tex]\(m\)[/tex], until the sales, [tex]\(s\)[/tex], are the same for both headband styles is:
[tex]\[
s = 40 \times (1.1)^m
\][/tex]
[tex]\[
s = 20 \times (1.15)^m
\][/tex]
Thus, the correct answer is:
C. [tex]\( s = 40 \times (1.1)^m \)[/tex]
[tex]\( s = 20 \times (1.15)^m \)[/tex]
